document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012281>Question 1012281</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i would like to receive help with this question. \" A cylindrical shaped cup has a height of 7 centimeters  and a volume of 112 pi cubic centimeters. Henry fills the cup completely full of water. He then pours the water from the cup into a cone. If the cone has a radius twice the measure of the cup, What is the height of the cone? \"  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628171 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=628171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cylinder height = 7 cm and volume - 112 * pi cubic cm.\r<BR>\n" );
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document.write( "henry fills the cup with water all the way to the top.\r<BR>\n" );
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document.write( "he then pours all the water into a cone.\r<BR>\n" );
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document.write( "presumably this also fills up the cone.\r<BR>\n" );
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document.write( "the cone has double the radius of the cylinder.\r<BR>\n" );
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document.write( "what is the height?\r<BR>\n" );
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document.write( "the volume of the cone must be the same as the volume of the cylinder.\r<BR>\n" );
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document.write( "the formula for the volume of a cone is v = 1/3 * pi * r^2 * h\r<BR>\n" );
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document.write( "the radius of the cone is twice the radius of the cylinder.\r<BR>\n" );
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document.write( "the radius of the cylinder is is not provided so we have to solve for it.\r<BR>\n" );
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document.write( "the formula for the volume of a cylinder is pi * r^2 * h.\r<BR>\n" );
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document.write( "since the volume is 112, the formula becomes 112 = pi * r^2 * 7, because the height is given as 7 cm.\r<BR>\n" );
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document.write( "we can solve for r^2 to get r^2 = 112 / (pi * 7) which becomes r^2 = 16 / pi.\r<BR>\n" );
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document.write( "solve for r to get r = 4 * sqrt(pi).\r<BR>\n" );
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document.write( "since the radius of the cone is twice the radius of the cylinder, then the radius of the cone is 8 * sqrt(pi).\r<BR>\n" );
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document.write( "we get formula for the volume of the cone becomes 112 = 1/3 * pi * (8 * sqrt(pi))^2 * h\r<BR>\n" );
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document.write( "solve for h to get h = 112 / (1/3 * (8 * sqrt(pi))^2)\r<BR>\n" );
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document.write( "simplify to get h = (112 * 3) / (64 * pi) which becomes h = 336 / (64 * pi) which becomes h = 5.25 cm.\r<BR>\n" );
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document.write( "so, we have:\r<BR>\n" );
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document.write( "r for the cylinder = 4/sqrt(pi)<BR>\n" );
document.write( "h for the cylinder = 7\r<BR>\n" );
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document.write( "r for the cone = 8/sqrt(pi)<BR>\n" );
document.write( "h for the cylinder = 5.25\r<BR>\n" );
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document.write( "volume for each = 112.\r<BR>\n" );
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document.write( "formula for volume of a cylinder is v = pi * r^2 * h.<BR>\n" );
document.write( "v = 112<BR>\n" );
document.write( "r = 4/sqrt(pi), r^2 = 16/pi<BR>\n" );
document.write( "h = 7<BR>\n" );
document.write( "formula becomes 112 = pi * 16/pi * 7 = 16 * 7 = 112.<BR>\n" );
document.write( "this checks out ok.\r<BR>\n" );
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document.write( "formula for volume of a cone is v = 1/3 * pi * r^2 * h.<BR>\n" );
document.write( "v = 112<BR>\n" );
document.write( "r = 8/sqrt(pi), r^2 = 64/pi<BR>\n" );
document.write( "h = 5.25<BR>\n" );
document.write( "formula becomes 112 = 1/3 * pi * 64/pi * 5.25 = 1/3 * 64 * 5.25 = 112.<BR>\n" );
document.write( "this checks out ok as well.\r<BR>\n" );
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document.write( "your solution is that the height of the cone is 5.25 centimeters.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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